Question

A tree is broken by wind and its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of 45$^\circ$ with the ground. The entire length of the tree is

• A. 15 m
• B. 20 m
• C. 10(1 +$\sqrt {2}$) m
• D. 10(1 +$\frac {\sqrt {2}} {3}$) m

Answer 1

Answer: (B)

20 m

Answer 2

Let AC denote the tree and let it be broken at the point B. Let it touch the ground at D. Thus AD = 10 metres Also $\frac{AB}{AD}$ = tan $45^\circ$ = 1 $\therefore$ AB = AD = 10 metres. Also BC = BD = $\sqrt{(10)^2 + (10)^2}$ = $10 \sqrt{2}$ AC = 10 + $10 \sqrt{2} = 10 ( \sqrt{2} + 1)$ metres.